A body is executing `SHM` under action of the a force of whose maximum is `50 N`. magnitude of force acting on the particle at the time when its energy is half kinetic energy and half potential is (Assume potential energy to be zero at mean position).

Explanation

Total energy of oscillation, `E = 1//2 m a^(2) omega^(2)`
Given `U = K implies (1)/(2) (m omega^(2)) x^(2) = (1)/(2) mv^(2)`
`:. (1)/(2) mA^(2) omega^(2) sin^(2) omega t = (1)/(2) mA^(2) omega^(2) cos^(2) omega t`
or `tan^(2) omega = 1 implies omega t = (pi)/(4)`
But `a = - omega^(2) x`
`= - omega^(2) A sin omega t`
Hence force acting on the partical at this time is
`|F| = ma = m omega^(2) A sin (pi)/(4)` (in the same of magnitude)
But `F_(max) = m omega^(2) A = 50 N`
`:. F = (50)/(sqrt2) = 25sqrt2 N`